Preheat the oven to 350˚ F.
Line 2 baking sheets with parchment paper or silicone baking mats. In a large bowl, cream the butter and both sugars together well until fluffy. Add in egg and vanilla extract.
In a separate large bowl, whisk together the flour, cocoa powder, baking soda, and salt. Add the dry ingredients into the wet ingredients, one cup at a time, with a rubber spatula until just incorporated. The dough will look and feel a little dry, this is when you mix in the milk and fold in the Andes baking chips and chocolate chips.
Let dough chill for a minimum of 1 hour to overnight.
Using a small cookie scoop or a spoon to roll about 2 tablespoon of dough into balls, place cookie dough on the baking sheets.
Bake 10 minutes. Let cool on the baking sheets for about 5 minutes, then transfer to a wire rack to cool completely.
Keep in an airtight container for 3-4 days.